python谐波运动动画

Question

I am trying to plot an animation of a simple pendulum using the model https://matplotlib.org/gallery/animation/double_pendulum_sgskip.html .

My code is as follows :

from numpy import sin, cos
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import matplotlib.animation as animation

#some constants 
g = 9.81 
l = 0.1 
m = 0.01 

def sh(r,t):
    theta = r[0]
    omega = r[1]
    sh_theta = omega
    sh_omega = -g/l*sin(theta) 
    return np.array([sh_theta,sh_omega],float)

init_state = [np.radians(89.0),0]
time = np.arange(0,50.0,0.025)
time_elapsed = time

def step_solver(eq, ist, dt):

    """
    Execute one time step of length dt and update status

    """
    global time_elapsed 

    state1,state2 = integrate.odeint(eq,ist,[0,dt])
    time_elapsed += dt

    return state1, state2,time_elapsed
dt = 1/30
ysol,ysolv,timex = step_solver(sh,init_state,dt)
print("This is the y0 values: ", ysol,"y values",ysolv,"This is the time ", timex) 

##===================================
##Setting up figure and animation 
#======================================
fig = plt.figure()
ax = plt.axes(xlim = (0,2), ylim = (-2,2))
line, = ax.plot([],[],lw=2)
#time_text = ax.text(0.02,0.95,'',transform = ax.transAxes) 
#==========================================
##initialisation function: plot the background of each frame 
def init():
    line.set_data([],[])
    #time_text.set_text('')
    return line, 

def animate(ysol,timex):

    x = timex 
    y = ysol

    line.set_data(x,y)
    #time_text.set_text(str(i))
    return line,
#================================================
#Call the animator    
#================================================
anim = animation.FuncAnimation(fig,animate(ysolv,timex), init_func = init, frames = 200, interval =20, blit = True)
anim.save('basic_animation.mp4', fps=30, extra_args=['-vcodec', 'libx264'])
plt.show()

EDIT : I am getting the error message :

  ValueError: shape mismatch: objects cannot be broadcast to a single shape

  <Figure size 432x288 with 1 Axes>

I have checked what my function step_solver is printing with

 print(len(ysol),len(ysolv),len(timex))

and after recommendation the other y output for odeint which gave only 2 values for my ysol and ysolv variable for 2200 time values.

I was expecting to get a range of y values for each time step. I am not sure how to sort this. Is my function step_solver wrongly coded? Why am I only getting 2 values, how can I animate the solution in the same way it was done for the double pendulum?

Any suggestions on where the problem may lie? Many thanks in advance.

Answer 1

Let's follow the code from the example more closely. Which means to use just one integration call and then using slices of the result of that call in the animation.

from numpy import sin, cos
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import matplotlib.animation as animation

#some constants 
g = 9.81 
l = 0.1 
m = 0.01 

def sh(r,t):
    theta, omega = r
    sh_theta = omega
    sh_omega = -g/l*sin(theta) 
    return np.array([sh_theta,sh_omega],float)

init_state = np.radians([89.0,0])
dt = 1.0/30
time = np.arange(0,50.0,dt)

state = integrate.odeint(sh,init_state,time)

##===================================
##Setting up figure and animation 
#======================================
fig = plt.figure()
ax = plt.axes(xlim = (0,10), ylim = (-2,2))
line, = ax.plot([],[],lw=2)
#==========================================
##initialisation function: plot the background of each frame 
def init():
    return line, 

def animate(i):

    x = time[i:i+30] 
    y = state[i:i+30,0]

    line.set_data(x,y)
    return line,
#================================================
#Call the animator    
#================================================
anim = animation.FuncAnimation(fig,animate, init_func = init, frames = 200, interval =20, blit = True)
plt.show()

For a variant using a step generator using yield see my answer in Error in RK4 algorithm in Python . This allows to encapsulate the data for the integration loop without defining a class for it. However it is not clear how a function graph with two samples would be helpful, even if it is animated.

To animate the pendulum itself, use

##===================================
##Setting up figure and animation 
#======================================
fig = plt.figure(figsize=(8,6))
ax = plt.axes(xlim = (-2*l,2*l), ylim = (-2*l,l))
line, = ax.plot([],[],'-o',lw=2,ms=8)
#==========================================
##initialisation function: plot the background of each frame 
def init():
    return line, 

def animate(i):

    phi = state[i,0]

    line.set_data([0,l*sin(phi)],[0,-l*cos(phi)])
    return line,
#================================================
#Call the animator    
#================================================
anim = animation.FuncAnimation(fig,animate, init_func = init, frames = len(time), interval =100, blit = True)
plt.show()